Discourse analysis, as Murcia and Olshtain (2000) assume, is a vast study of language in use that extends beyond sentence level, and it involves a more cognitive and social perspective on language use and communication exchanges. Holding a wide range of phenomena about language with society, culture and thought, discourse analysis contains various approaches: "speech act", "pragmatics", "conversation analysis", "variation analysis", and "critical discourse analysis". Each approach works in its different domain to discourse. For one dimension, it shares the same assumptions or general problems in discourse analysis with the other approaches: for instance, the explanation on how we organize language into units beyond sentence boundaries, or how language is used to convey information about the world, ourselves and human relationships (Schiffrin 1994: viii). For other dimensions, each approach holds its distinctive characteristics contributing to the vastness of discourse analysis. This paper will mainly discuss two approaches to discourse analysis--"conversation analysis" and "speech act theory"-- and will attempt to point out some similarities as well as contrasting features between the two approaches, followed by a short reflection on their strengths and weaknesses in the essence of each approach. The organizational and discourse features in the exchanges among three teachers at the College of Finance and Customs in Vietnam will be analysed in terms of conversation analysis and speech act theory.